March 28, 2016
The Woods-Saxon potential is
where is the half-maximum radius that is the reduced radius and is the nuclear mass number, and is the diffusiveness parameter.
The root-mean-squared (rms) radius is
where the “extract” is because of spherical coordinate.
The integration is a polynomial
In mathematica, the sum is notated by,
Thus, the rms radius for is
For , ,
February 16, 2011
16O, 28Pb, Fermi, fm, Woods-Saxon
this is a collective model of the nuclei density vs radius. it has another name Fermi-shape.
where is central density, or density at r = 0. is the radius of half density and is the diffuseness. when a is large, the “tail” of the shape will be longer.
the radius is measured in unit of fm .
can be vary from 1 fm to 7 or 8 fm. for 16O, it is about 2 fm. and for 208Pb, it is about 6fm .
is more or less the same for different nuclei.
the density of nuclei can be mass density or charge density, the Woods-Saxon also gives a good approximation.
for mass density, a . for comparison, water density is 1 kg per meter cube.
and charge density is about .